GRADE/GRAAD 12 JUNE/JUNIE 2017 …

1 NATIONAL/NASIONALE. SENIOR. CERTIFICATE/SERTIFIKAAT. GRADE/GRAAD 12. JUNE/JUNIE 2017 . mathematics P2/ wiskunde V2. memorandum . MARKS/PUNTE: 150. This memorandum consists of 12 pages. Hierdie memorandum bestaan uit 12 bladsye. 2 mathematics P2 / wiskunde V2 (EC/JUNE 2017 ). QUESTION 1 / VRAAG 1. Percentages / Frequency / Cumulative Frequency / 3, 12. Persentasies Frekwensie Kumulatiewe Frekwensie 30 < 40 1 1 24, 35, 44. 40 < 50 2 3. 50 < 60 9 12 50. 60 < 70 12 24. 70 < 80 11 35. 80 < 90 9 44. 90 < 100 6 50 (3).

2 Ogive 55. upper limits / bo-limiete 50. 45. 40 cum f / kum. f Cummulative Frequency 35. shape / vorm 30 B. grounded / ge-anker 25. 20. 15. 10. 5. 0. 0 10 20 30 40 50 60 70 80 90 100 110. Percentages (4). Approx. 30 [accept between 28 32] answer/ indicated on Ongeveer 30 [aanvaar tussen 28 32] graph. antwoord / op grafiek aangedui (2). [9]. QUESTION 2 / VRAAG 2. 12,4 15,1 18,9 19,7 19,7 20,0. 20,9 23,7 23,8 31,1 33,6 34,5. 34,9 36,5 40,1. Minimum / Minimum = min & max Lower quartile / Onderste kwartiel (Q1) = Q1.

3 Median / Mediaan (Q2) = Q2. Upper quartile / Boonste kwartiel (Q3) = Q3. Maximum / Maksimum = (4). Copyright reserved Please turn over (EC/ junie 2017 ) wiskunde V2 / mathematics P2 3. min / max Q1 / Q3. Q2 (3). Skewed positively to the right. positively skewed /. Skeef positief na regs positief skeef (1). SD/SA = 8,36 answer / antwoord (2). A small standard deviation indicates that the data is clustered answer / antwoord around the mean. OR/OF. A large standard deviation indicates that the data is more spread out.

4 Klein standaardafwyking dui aan dat die data rondom die gemiddelde gegroepeer is. Groot standaardafwyking dui aan dat die data meer versprei is. (1). [11]. QUESTION 3 / VRAAG 3. R S. M=[ 2 ;. 6+8 9 1. ] x- value of M / x-waarde van M. 2 y- value of M / y-waarde van M. M = (7 ; 4). (2). mFM = 7 4 =. 4 3 1 substituting / vervanging 3. value of mFM / waarde van mFM. 1 1. 1 = 3 ( 1 ) m=3. 1. y 4 = 3(x 7) M = (7; 4) substituting M(7; 4) / vervanging M(7; 4). 1 5. y= x+ answer / antwoord 3 3. (4). Kopiereg voorbehou Blaai om asseblief 4 mathematics P2 / wiskunde V2 (EC/JUNE 2017 ).

5 1 5 substitution into line equation / vervanging in lyn vergelyking 1= +. 3 3 answer (as negative) / antwoord (as negatief). t = -2. OR / OF. OR / OF. mAF = mFM. 3 1 1 substitution into grad eqn / vervanging in gradi nt vergelyking =. 4 3 answer as negative / antwoord as negatief (2). 4 t=6. t = -2. mPC =. 3 ( 1). = -1 substitution / vervanging 4 8 answer / antwoord ANSWER ONLY. FULL MARKS/. SLEGS ANTWOORD. (2). tan = -1 tan = -1. = 135 = 135 (2). 2 1 1. tan = 10 = 5 tan = 5. = 180 = = .. = . = = . answer / antwoord (4).

6 [16]. QUESTION 4 / VRAAG 4. 7 1 1 5. C =[ 2 ; 2 ] x-value /waarde ANSWER ONLY / SLEGS ANTWOORD y-value /waarde (2). = [3; 2]. Copyright reserved Please turn over (EC/ junie 2017 ) wiskunde V2 / mathematics P2 5. CA2 =(3 0)2 + (2 + 2)2 substitution / substitusie CA2 = 25. CA = 5 answer for CA. antwoord vir CA. CB2 = (7 3)2 + (1 + 2)2. CB2 = 25. CB = 5 answer for CB. CA = CB antwoord vir CB (3). 2 5 substitution m AD m AD 7. 0 1. 7. 2 1. m AB substitution 0 7. 1 m AB.. 7. 1 m AD m AB 1. m AD m AB 7 1. 7 (5).

7 AD AB [m AD m AB 1]. DA B 900. ( 3)2 + ( + 2)2 = 25 correct centre /. korrek middelpunt correct / korrekte r2 (2). 1 2 . mBC substitution 7 3. 3. m BC (2). 4. 4 mtan mtan= 3. 4. subst m= 3 and B(7;1). 4. 1 = ( 7) 4. verv. m= 3 en B(7;1). 3. 4 31 answer / antwoord (3). = +. 3 3. AE DB [diametersof same circle] AE = DB reason ABED is a rectangle [diagonals ]. reason (3). [20]. QUESTION 5 / VRAAG 5. sin 238 = sin 58 reduction / reduksie = k answer / antwoord (2). cos 58 = sin 32 . = 1 2 sin 32 . answer / antwoord (2).

8 Kopiereg voorbehou Blaai om asseblief 6 mathematics P2 / wiskunde V2 (EC/JUNE 2017 ). tan(180 30 ).sin(360 60 ).sin 10 - tan 30 . =. cos(180 +45 ).sin(180 45 ).cos( 90 10 ) - sin 60 . - cos 45 . =. ( tan 30 )( sin 60 ) sin 10 sin 45 . ( cos 45 )(sin 45 ) sin 10 sin 10 . 1 3.. simplification /. 3 2 vereenvoudiging = 1 1.. 2 2. = -1 answer / antwoord (7). sin( + ) = cos [ 90 ( + )] cos [ 90 ( + )]. = cos[(90 ) ] cos[(90 ) ]. = cos(90 ) cos sin(90 ) cos(90 ) cos sin(90 ) . = sin cos cos sin sin cos cos sin (4).

9 Cos 2 + 1 2 cos 2 1 + 1 identity numerator = identiteit teller sin 2 . tan sin . 2 sin cos . identity denominator cos identiteit noemer 2 2 sin . = . cos . 2 2 . 2 . 1 2 simplification /. =. 2 vereenvoudiging (4). sin sin . identity / identiteit (cos ). = 2 sin . cos . sin = 2 sin cos . sin 2 sin cos = 0. simplification /. vereenvoudiging sin (1 2 cos ) = 0. 1 factors / faktore sin = 0 or/of cos = (3). 2. sin = 0 1. or cos = 2 = 0 . = 0 + 360 , = 180 . OR = 60 + 360 = 60 . = 180 + 360 360 , (4). [26]. Copyright reserved Please turn over (EC/ junie 2017 ) wiskunde V2 / mathematics P2 7.

10 QUESTION 6 / VRAAG 6. Asymptotes / Asimptote ( f ) Shape / Vorm ( g ). (45 ; 1) ( f ) (-45 ; 0) / (135 ; 0) / x-intercepts ( g ). Endpoints / Eindpunte ( f ) Endpoints / Eindpunte ( g ). (6). x = -45 -45 . (2). (-90 ;45 ] OR/OF 90 x 45. 0 0. 90 and 45. 0 0. correct inequalities (2). 90 answer / antwoord (1). [11]. QUESTION 7 / VRAAG 7. In ABC. AC . ANSWER ONLY/ proportion / verhouding =. sin sin SLEGS ANTWOORD..sin . AC = answer / antwoord (2). Kopiereg voorbehou Blaai om asseblief 8 mathematics P2 / wiskunde V2 (EC/JUNE 2017 ).)